Table of Contents

Last modified on August 3rd, 2023

The surface area, or total surface area (TSA), of a hexagonal pyramid, is the entire space occupied by its seven faces. It is measured in square units such as m^{2}, cm^{2}, mm^{2}, and in^{2}.

The formula is given below:

The formula to calculate the surface area of a hexagonal pyramid also includes its lateral surface area (LSA).

**Lateral Surface Area ( LSA)**

∴ **Total Surface Area ( TSA) = 3ab + LSA**

Let us solve some examples to understand the concept better.

**Find the lateral and total surface areas of a hexagonal pyramid with a base of 5 cm, an apothem of 4.33 cm, and a slant height of 9 cm.**

Solution:

As we know,

Lateral Surface Area (*LSA*) = 3bs, here b = 5 cm, s = 9 cm

∴ *LSA* = 3 × 5 × 9

= 135 cm^{2}

Total Surface Area (*TSA*) = 3ab + *LSA,* here a = 4.33 cm, b = 5 cm, *LSA *= 135 cm^{2}

∴*TSA* = 3 × 4.33 × 5 + 135

= 199.95 cm^{2}

Finding the surface area of a hexagonal pyramid when the **BASE** and **HEIGHT** are known

**Find the surface area of a hexagonal pyramid with a base of 4 cm, and a height of 6 cm.**

Solution:

We will use an alternative formula for finding the surface area of a hexagonal pyramid.

Total Surface Area (*TSA*) = ${\dfrac{3\sqrt{3}}{2}b^{2}+3b\sqrt{h^{2}+\dfrac{3b^{2}}{4}}}$, here b = 4 cm, h = 6 cm

∴ *TSA* = ${\dfrac{3\sqrt{3}}{2}\times 4^{2}+3\times 4\times \sqrt{6^{2}+\dfrac{3\times 4^{2}}{4}}}$

= 124.71 cm^{2}

Last modified on August 3rd, 2023

Why exactly does the alternative formula work?

It works as the basic formula cannot be applied here.